Question

A uniform, solid, 1000 kg sphere has a radius of 5 m. Find the gravitational force this sphere exerts on a 2 kg point mass placed at a distance of 5.01 m from the center of the sphere?​

Answer 1

I don’t know the answer

Answer 2

The Gravitational force is 5.23 x 10 ∧ -9 N

Given :

mass of solid sphere M = 1000kg ,

mass of the point mass m =2kg,

radius of sphere= 5 m.

To find : Gravitational force =?

Solution:

Point mass outside the solid sphere ,

the magnitude of gravitational force,

F=G M m/r² ;  r $\geq$R

The magnitude of force on the point mass is given by

F= GVmρ/ r² = G M m r/R³ ;

V=4/3πr³ ;

ρ= M/V.

So, we have two cases,

case 1: for r $\geq$R      F=G M m/r²

case 2: for r$\leq$R      F=G M m r/R³

so, our question asks for

case 1 as r $\geq$R = (5.01 >5)

By putting values,

F=G M m/r²

F=5.23 x 10 ∧ -9 N

Therefore , gravitational force is F=5.23 x 10 ∧ -9 N